POWER OF ATTORNEY

    Know all by these presents, that the undersigned hereby constitutes and
appoints each of (i) the Secretary of Lonestar Resources US Inc., a Delaware
corporation (the "Company"), who is currently Chase Booth, (ii) the Company's
Chief Accounting Officer, who is currently Jason Werth and (iii) the Company's
Chief Executive Officer, who is currently Frank D. Bracken, III, and their
respective successors, signing singly, with full power of substitution, as the
undersigned's true and lawful attorney-in-fact to:

    (1) execute for and on behalf of the undersigned, in the undersigned's
        capacity as an officer and/or director of the Company, Forms 3, 4 and 5
        (including amendments thereto) in accordance with Section 16(a) of the
        Securities Exchange Act of 1934 and the rules and regulations thereunder
        and a Form ID, Uniform Application for Access Codes to File on EDGAR;

    (2) do and perform any and all acts for and on behalf of the undersigned
        which may be necessary or desirable to complete and execute any such
        Forms 3, 4 or 5 or Form ID and timely file such forms (including
        amendments thereto) and application with the United States Securities
        and Exchange Commission and any stock exchange or similar authority; and

    (3) take any other action of any type whatsoever in connection with the
        foregoing which, in the opinion of such attorney-in-fact, may be of
        benefit to, in the best interest of, or legally required by, the
        undersigned, it being understood that the documents executed by such
        attorney-in-fact on behalf of the undersigned pursuant to this Power of
        Attorney shall be in such form and shall contain such terms and
        conditions as such attorney-in-fact may approve in such attorney-in-
        fact's discretion.

    The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in- fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

    The undersigned agrees that each such attorney-in-fact herein may rely
entirely on information furnished orally or in writing by the undersigned to
such attorney-in-fact.  The undersigned also agrees to indemnify and hold
harmless the Company and each such attorney-in-fact against any losses, claims,
damages or liabilities (or actions in these respects) that arise out of or are
based upon any untrue statements or omission of necessary facts in the
information provided by the undersigned to such attorney-in fact for purposes of
executing, acknowledging, delivering or filing Forms 3, 4 or 5 (including
amendments thereto) or Form ID and agrees to reimburse the Company and such
attorney-in- fact for any legal or other expenses reasonably incurred in
connection with investigating or defending against any such loss, claim, damage,
liability or action.

    This Power of Attorney supersedes any power of attorney previously executed
by the undersigned, in the undersigned's capacity as an officer and/or director
of the Company, regarding the purposes outlined in the first paragraph hereof
("Prior Powers of Attorney"), and the authority of the attorneys-in-fact named
in any Prior Powers of Attorney is hereby revoked.

    This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 or 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier (a) revoked by the undersigned in a signed writing delivered to
the foregoing attorneys-in-fact or (b) superseded by a new power of attorney
regarding the purposes outlined in the first paragraph hereof dated as of a
later date.

    IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 10th day of December, 2020.

                                            /s/ Richard Burnett
                                           --------------------------
                                           Richard Burnett

















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